In this study, we take into account the aforementioned uncertainties and/or corrections from nuclear physics, hadron physics, elementary particle physics, i.e., nucleon form factor (free space and medium), and NMM and NCR in the description of neutrino electro-weak interaction at finite density and zero temperature. The values of the NMM and NCR are obtained from experimental constraints [1]}, [2]}. We then calculate the differential cross-section (DCS) for the neutrino-nucleon scattering and NMFP of the neutrinos in the core of the NS. The roles of the nucleon and neutrino corrections in the neutrino propagation inside NS are explored in further detail. We find that the in-medium corrections of the nucleon form factor and NCR give a significant impact on the DCS and NMFP. Compared to the vacuum nucleon form factor (VFF), the density dependence of the nucleon form factor (DDFF) decreases the DCS, implying an increase in the NMFP. The increase of the NMFP is more significant at higher matter density. It means that the neutrino with the DDFF will more freely escape from the core of NS. By taking an NMM value from the experimental constraints [1]}, the DCS does not change significantly. This indicates that the NMM plays a small role in the neutrino emission from the NS core. However, it is drastically changed when we consider a finite NCR value, which is obtained from the experiment constraint [2]}. It increases the DCS significantly in comparison with other scenarios without the NCR. This shows that the neutrinos are more strongly interacting with the matter if the NCR contribution is taken into account appropriately.
